Emergent Mind
Strong Brascamp-Lieb Inequalities
(2102.06935)
Published Feb 13, 2021
in
math.FA
,
cs.IT
,
math.IT
,
and
math.PR
Abstract
In this paper, we derive sharp nonlinear dimension-free Brascamp--Lieb inequalities (including hypercontractivity inequalities) for distributions on Polish spaces, which strengthen the classic Brascamp--Lieb inequalities. Applications include the extension of Mrs. Gerber's lemma to the cases of R\'enyi divergences and distributions on Polish spaces, the strengthening of small-set expansion theorems, and the characterization of the exponent of the $q$-stability. Our proofs in this paper are based on information-theoretic and coupling techniques.
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